Issue 3

JTAM, Sofia, vol. 3 Issue 3 (1972)

Electromechanical Interaction in Viscoelastic Media

G. Brankov, N. Petrov
Bulgarian Academy of Sciences, 7 Noemvri 1, Sofia

The constitutive equations of a continuous viscoelastic medium, allowing electromechanical interaction, are studied in the presented paper. The validity of the basic principles – the principle of causality, the first and the second principles of thermodynamics, is accepted. The assumptions that: the system is linear, smooth and invariant in time, are considered valid for the system. By means of the apparatus of general system theory are obtained the differential and integral form of the constitutive equations, the general equation of heat conductivity and the functional expressions for the free energy, the total internal energy and the dissipative work.

JTAM, Sofia, vol. 3 Issue 3 pp. 009-027 (1972), [Full Article]

Propagation of Elastic Waves in Circular Cylinder Subject to Finite Deformation, Incompressible Material

M. Kozarov, Al. Rachev, Ts. P. Ivanov
Institute of Technical Mechanics, Sofia

The propagation of elastic waves with small amplitudes in circular cylinder subject to finite, isothermal and homogeneous deformation is considered in the presented paper. The material is supposed hyperelastic, isotropic, incompressible and generally non-linear. The equations of motion are deduced for the cases when the superposed small dynamic deformation is accepted isothermal or adiabatic. The corresponding equations for determination of the phase velocities of wave propagation are obtained. The partial cases for longitudinal, torsional and flexural waves are obtained from the deduced results. The effect of the preliminary deformation on the phase velocities for some partial forms of the elastic potential is studied.

JTAM, Sofia, vol. 3 Issue 3 pp. 029-044 (1972)

On Integration of the Basic System of Partial Differential Equations for the Different Modular Elasticity Theory

I.T. Minchev, H.N. Karanikolov
Higher Institute of Mining and Geology, Sofia

The basic equations for the different modular elasticity theory are deduced in displacements for the continuous anisotropic media of most general type. These equations represent a system of nonhomogeneous partial differential equations with functional coefficients. Integration of this system of equations at definite boundary conditions is done via introduction of a new function φ(x, y) which is continuous and differentiable in the considered region and can be developed as a functional power series. For determination of the functional coefficients of this power series the necessary number of algebraic equations are obtained. The solution for the case of plane state of strain of the considered continuous media is given in details. It is shown that the solutions when the medium is different modular, orthogonal anisotropic, transversally isotropic and totally isotropic, but different modular, can be obtained as partial cases.

JTAM, Sofia, vol. 3 Issue 3 pp. 045-050 (1972)

Canonical Equations of the Force Method of the Nonlinear Structural Mechanics

R.K. Malenov
Higher Institute of Civil Engineering, Sofia

The problem of the nonlinear-elastic frame systems (elasto-plastic frames at simple and monotonic loading) is formulated as problem of Lagrange from the theory of the optimal solutions or as a problem of the non-linear programming. The canonical equations are obtained of the force method of the nonlinear structural mechanics. Along with frames whose material resists equally strain and pressure armoured concrete frames are also surveyed.

JTAM, Sofia, vol. 3 Issue 3 pp. 051-056 (1972)

Classes of Motions with Screw Axes Forming Stratifiable Couple of Congruences

V. Diamandiev
Faculty of Mathematics, Sofia University, Sofia

The paper reports on the relations established, which exist in most ge¬neral type between the kinematic elements of two classes of motion whose screw axes form stratifiable couple of congruences. The conditions for stratification are obtained from the definition providing that the tangential planes towards the stratifying surfaces of the one congruence should comprise the straight line of the other congruence. These conditions are equivalent to six equations. It is pointed out that in a particular case these six equations may be reduced to two. Thus, a case of stratifiable couple of congruences is obtained whose common perpendicular forms a star of straight lines.

JTAM, Sofia, vol. 3 Issue 3 pp. 057-060 (1972)

Eccentric Impact of Rough Bodies – Problems, Hypotheses, Results from Experimental Investigations

L. Stoimenov

Certain problems are surveyed arising at putting into practice the applied theory of the centric impact in the case of eccentric impact of rough bodies. The possible flagrant errors at such application are investigated. Experimental results are presented from tests on eccentric impact of rough bodies.

JTAM, Sofia, vol. 3 Issue 3 pp. 061-072 (1972)

Application of Kinematic Variable Basic System

N.V. Kardzhiev
Higher Institute of Civil Engineering, Sofia

The method is applied to hinged steel bar system which may comprise steel ropes as well. The kinematic variable constructions are not excluded. The geometrical and physical nonlinearity is taken into consideration. Use is made of kinematic variable basic system in which the force factors may be simply determined from the projection equilibrium conditions. It is pointed out that these vectors are linear combinations of the unknown quantities. The general canonical equations of the force method are deduced, in which the strain designations are given. Earlier the method is applied by the author for calculation of steel rope systems. It is pointed out that the equations express the conditions of stationariness of a scalar function, representing additional work. It is obtained in the form of difference of two convex functions by means of which the non-uniqueness of the solution is possible.

JTAM, Sofia, vol. 3 Issue 3 pp. 073- (1972)